It is well known that skilled bicycle riders can balance and propel themselves forward using motions of the handlebar. We present the complete nonlinear dynamics and control of such a pedal-less bicycle with a rider. Propulsion is achieved not by pedaling but by a cyclic motion of the steering axis of the bicycle. It is shown that this kind of actuation results in net forward motion of the bicycle and a building up of momentum. The dynamics of the bicycle and rider in a transverse plane are similar to that of a two link underactuated system where only the second link is actuated. A linear analysis of the bicycle is used to derive a control law for the rider to stabilize the bicycle about its upright position while the periodic motion of the steering axis drives the bicycle forward. After the bicycle attains a higher speed, it is easily stabilizable.

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